Mon, October 16, 2017
Public Access

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11:00am [11:30am] Madhusudan Manjunath
Title: Free Resolutions of Monomial Ideals III. Abstract: We continue the study of resolutions of monomial ideals. We start with a short proof of the exactness of the Koszul complex. We then generalize this to free resolutions of any monomial ideal. We'll conclude with the proof of the Hilbert syzygy theorem and some more examples of monomial ideals.

2:00pm [2:30pm] Ashwin Deopurkar, TIFR Mumbai
Title: Tropical geometry of curves Abstract: Perhaps surprisingly, the study of degenerate curves plays a crucial role in our understanding of a general smooth curve. One of the first successes of this idea was the theory of limit linear series developed by Griffiths and Harris which they used to prove the Brill-Noether theorem. The analogous theory for degenerate curves of non-compact type falls in the realm of tropical geometry where it takes the shape of metric graphs (or tropical curves) and divisors on them. This leads to a rich interplay between graph theory and algebraic geometry of curves. After explaining the central ideas we will discuss some applications to Brill-Noether theory and curves of large theta characteristic.

4:00pm [4:00pm] Dr Amey Deshpande, University of Pune
Title: Developments in Fractional Dynamical Systems Abstract: Fractional calculus (FC) is witnessing rapid development in recent past. Due to its interdisciplinary nature, and applicability it has become an active area of research in Science and Engineering. Present talk deals with our work on fractional order dynamical systems (FODS), in particular on local stable manifold theorem for FODS. Further we talk on bifurcation analysis and chaos in the context of FODS. Finally we conjecture a generalization of Poincare-Bendixon for fractional systems.